The asymptotic controllability of the identified system is a central problem in adaptive control. if controllability is ascertained, the analysis of even complex adaptive controllers based on multistep performance indices is drastically simplified. In this paper, we study the controllability issue in connection with the recursive least-squares (RLS) algorithm. We show that standard RLS does not generally provide models that are controllable. However, a variant of this method that preserves all the basic properties of the standard RLS and also guarantees asymptotic controllability is introduced. The algorithm can be safely used in any adaptive control system, provided that the control law is able to stabilize known invariant plants.